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This paper propose the concept of big model as a novel research paradigm for regional and urban studies. Big models are fine-scale regional/urban simulation models for a large geographical area, and they overcome the trade-off between…
Distance covariance and distance correlation are scalar coefficients that characterize independence of random vectors in arbitrary dimension. Properties, extensions, and applications of distance correlation have been discussed in the recent…
Large, data centric applications are characterized by its different attributes. In modern day, a huge majority of the large data centric applications are based on relational model. The databases are collection of tables and every table…
Spatial dependency and spatial embedding are basic physical properties of many phenomena modeled by networks. The most indicated computational environment to deal with spatial information is to use Georeferenced Information System (GIS) and…
Many growth processes lead to intriguing stochastic patterns and complex fractal structures which exhibit local scale invariance properties. Such structures can often be described effectively by space-time trajectories of interacting…
A holistic view of the cosmological appearance and development of space is obtained by studying space as a spherically closed surface of a 4-sphere in a zero energy balance between motion and gravitation. Such an approach re-establishes…
An analysis of high-dimensional data can offer a detailed description of a system but is often challenged by the curse of dimensionality. General dimensionality reduction techniques can alleviate such difficulty by extracting a few…
Current practice in parameter space exploration in euclidean space is dominated by randomized sampling or design of experiment methods. The biggest issue with these methods is not keeping track of what part of parameter space has been…
Some years ago we proposed a new approach to the analysis of galaxy and cluster correlations based on the concepts and methods of modern statistical Physics. This led to the surprising result that galaxy correlations are fractal and not…
Five fundamental scales of mass follow from holographic limitations, a self-similar law for angular momentum and the basic scaling laws for a fractal universe with dimension 2. The five scales correspond to the observable universe,…
Systems with lattice geometry can be renormalized exploiting their coordinates in metric space, which naturally define the coarse-grained nodes. By contrast, complex networks defy the usual techniques, due to their small-world character and…
Capturing human mobility is essential for modeling how people interact with and move through physical spaces, reflecting social behavior, access to resources, and dynamic spatial patterns. To support scalable and transferable analysis…
Four-dimensional(4D) spacetime structures are investigated using the concept of the geodesic distance in the simplicial quantum gravity. On the analogy of the loop length distribution in 2D case, the scaling relations of the boundary volume…
The scale-free (SF) structure that commonly appears in many complex networks is one of the hot topics related to social, biological, and information sciences. The self-organized generation mechanisms are expected to be useful for efficient…
This chapter explores the notion of "dimension" of a set. Various power laws by which an Euclidean space can be characterized are used to define dimensions, which then explore different aspects of the set. Also discussed are the…
The spatial pattern of urban-rural regional system is associated with the dynamic process of urbanization. How to characterize the urban-rural terrain using quantitative measurement is a difficult problem remaining to be solved. This paper…
Formerly the geometry was based on shapes, but since the last centuries this founding mathematical science deals with transformations, projections and mappings. Projective geometry identifies a line with a single point, like the perspective…
Distance correlation is a recent extension of Pearson's correlation, that characterises general statistical independence between Euclidean-space-valued random variables, not only linear relations. This review delves into how and when…
The laws of physics have a set of fundamental constants, and it is generally admitted that only dimensionless combinations of constants have physical significance. These combinations include the electromagnetic and gravitational fine…
Scale-free networks are abundant in nature and society, describing such diverse systems as the world wide web, the web of human sexual contacts, or the chemical network of a cell. All models used to generate a scale-free topology are…